Phys. Rev. D 66, 085025 (2002) [9 pages]Schrödinger representation for a scalar field on curved spacetimeReceived 25 July 2002; published 30 October 2002 It is generally known that linear (free) field theories are one of the few quantum field theories that are exactly soluble. In the Schrödinger functional description of a scalar field on flat Minkowski spacetime and for flat embeddings, it is known that the usual Fock representation is described by a Gaussian measure. In this paper, arbitrary globally hyperbolic spacetimes and embeddings of the Cauchy surface are considered. The classical structures relevant for quantization are used for constructing the Schrödinger representation in the general case. It is shown that, in this case, the measure is also Gaussian. Possible implications for the program of canonical quantization of midisuperspace models are pointed out. © 2002 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevD.66.085025
DOI:
10.1103/PhysRevD.66.085025
PACS:
03.70.+k, 04.62.+v
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